Active Learning for Undirected Graphical Model Selection

TL;DR

This paper introduces an active learning approach for graphical model selection that adaptively chooses measurements, reducing the total number needed compared to traditional passive methods.

Contribution

It presents a novel active learning algorithm using junction trees for graphical models, improving measurement efficiency over passive algorithms.

Findings

Active learning reduces measurement requirements.

Theoretical proof of fewer measurements needed.

Numerical results validate the approach.

Abstract

This paper studies graphical model selection, i.e., the problem of estimating a graph of statistical relationships among a collection of random variables. Conventional graphical model selection algorithms are passive, i.e., they require all the measurements to have been collected before processing begins. We propose an active learning algorithm that uses junction tree representations to adapt future measurements based on the information gathered from prior measurements. We prove that, under certain conditions, our active learning algorithm requires fewer scalar measurements than any passive algorithm to reliably estimate a graph. A range of numerical results validate our theory and demonstrates the benefits of active learning.